Techniques are known which acquire X-ray two-dimensional projections of an object by employing an X-ray device. Such 2D projections of the object find application in various medical fields, including, but not limited to visual guidance during interventions.
Often, a three-dimensional reconstruction is desirable to further obtain depth information of the object. In such a case, a given pixel of a 3D image may be associated with a 3D position in space. Techniques are known which enable to reconstruct the 3D image from a plurality of 2D projections, e.g. the so-called Feldkamp-Davis-Kress(FDK)-algorithm, see “Practical Cone-Beam Algorithm” by L. A. Feldkamp, L. C. Davis, and J. W. Kress in J. Opt. Soc. Am. A 1 (1984) 612. The FDK algorithm and various derivations thereof are sometimes referred to as analytic reconstruction techniques. Furthermore, different kinds of algebraic reconstruction techniques are known for the 3D reconstruction, see “Simultaneous algebraic reconstruction technique (SART): a superior implementation of the art algorithm” by A. H. Andersen and A. C. Kak in Ultrason Imaging (1984) 6 (1984) 81-94. Typically, a considerable number of 2D projections needs to be acquired for successfully reconstructing the 3D image. This may lengthen measurement time and/or increase an X-ray dose exposure. Furthermore, so-called compressed sensing techniques have evolved, see, e.g., “Improved Total Variation-Based CT Image Reconstruction Applied to Clinical Data” by L. Ritschl et al. in Phys. Med. Biol. 56 (2011) 1545 and “Prior Image Constrained Compressed Sensing (PICCS): A Method to Accurately Reconstruct Dynamic CT Images from Highly Undersampled Projection Data Sets” by G-H. Chen, J. Tang, and S. Leng in Med. Phys. 35 (2008) 660. Such compressed sensing techniques typically rely on a limited underlying data set of 2D projections on which the reconstruction is based, sometimes referred to as sparsified image data. Here it is possible that comparably fewer image pixels of the 2D projections have significant image values and/or that comparably fewer 2D projections are used for the reconstruction. In such a scenario, employing conventional algebraic and/or analytic reconstruction techniques may not be possible or only possible to a limited degree; such that, in effect, the compressed sensing techniques enable to shorten the measurement time and reduce the X-ray dose exposure if compared to the conventional algebraic and/or analytic reconstruction techniques.
Yet, such compressed sensing techniques face certain restrictions. E.g., employing compressed sensing techniques may result in the reconstructed 3D image to have an artificial look and being smoothed if compared to conventional analytic reconstruction techniques, such as the FDK algorithm. Sometimes, the 3D images obtained by a compressed sensing technique are referred to as being piecewise constant in homogeneous regions and as omitting small structures. For example, fine structures and features of the object may be lost in the 3D image. This may limit the medical applicability of compressed sensing techniques.